A Space–Time Code Design for CPM: Diversity Order and Coding Gain

Sufficient conditions are derived under which $M$-ary partial- and full-response continuous phase modulation (CPM) space–time (ST) codes will attain both full spatial diversity and optimal coding gain. General code construction rules are desirable due to the nonlinearity and inherent memory of the CPM signals which makes manual design or computer search difficult. Using a linear decomposition of CPM signals with tilted phase, we identify a rank criterion for $M$-ary partial- and full-response CPM that specifies the set of allowable modulation indices. We also propose a coding gain design criterion. Optimization of the coding gain for CPM ST codes is shown to depend on the CPM frequency/phase shaping pulse, modulation index, and codewords. The modulation indices and phase shaping functions that improve the coding gain are specified. Finally, optimization of coding gain for ST-CPM and orthogonal ST-CPM codewords is discussed.